The equation of a circle $C$ is $x^2+y^2-8x-10y+32 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Answer: To find the equation in standard form, complete the square. $(x^2-8x) + (y^2-10y) = -32$ $(x^2-8x+16) + (y^2-10y+25) = -32 + 16 + 25$ $(x-4)^{2} + (y-5)^{2} = 9 = 3^2$ Thus, $(h, k) = (4, 5)$ and $r = 3$.